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A company is preparing to make gold jewellery during a 2-month period for the Christmas season. It can make bracelets, necklaces, and pins. Each bracelet requires 6.3 ounces of gold and 17 hours of labour, each necklace requires 3.9 ounces of gold and 10 hours of labour, and each pin requires 3.1 ounces of gold and 7 hours of labour. The company has available 125 ounces of gold and 320 hours of labour. A bracelet sells for $1,650, a necklace for $850, and a pin for $790. If the company is aiming to maximize profit, what is the maximum profit it can achieve from making bracelets, necklaces, and pins using the resources currently at its disposal?      A. Objective value Z = 32460.47 B. Objective value Z = 32463.47 C. Objective value Z = 32461.47 D. Objective value Z = 32746.47

Question

A company is preparing to make gold jewellery during a 2-month period for the Christmas season. It can make bracelets, necklaces, and pins. Each bracelet requires 6.3 ounces of gold and 17 hours of labour, each necklace requires 3.9 ounces of gold and 10 hours of labour, and each pin requires 3.1 ounces of gold and 7 hours of labour. The company has available 125 ounces of gold and 320 hours of labour. A bracelet sells for 1,650,anecklacefor1,650, a necklace for 850, and a pin for $790. If the company is aiming to maximize profit, what is the maximum profit it can achieve from making bracelets, necklaces, and pins using the resources currently at its disposal?      A. Objective value Z = 32460.47 B. Objective value Z = 32463.47 C. Objective value Z = 32461.47 D. Objective value Z = 32746.47

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Solution

To find the maximum profit the company can achieve, we need to use linear programming.

Let's define the decision variables:

  • Let B represent the number of bracelets produced.
  • Let N represent the number of necklaces produced.
  • Let P represent the number of pins produced.

Now, let's set up the objective function to maximize profit: Maximize Z = 1650B + 850N + 790P

Next, we need to set up the constraints based on the available resources:

  • The amount of gold used cannot exceed the available 125 ounces: 6.3B + 3.9N + 3.1P ≤ 125
  • The amount of labor used cannot exceed the available 320 hours: 17B + 10N + 7P ≤ 320

Additionally, we have the non-negativity constraints: B ≥ 0, N ≥ 0, P ≥ 0

Now, we can solve this linear programming problem to find the maximum profit.

This problem has been solved

Similar Questions

The artisans at Jewellery Junction in Phoenix are preparing to make gold jewellery during a 2-month period for the Christmas season. They can make bracelets, necklaces, and pins. Each bracelet requires 6.3 ounces of gold and 17 hours of labour, each necklace requires 3.9 ounces of gold and 10 hours of labour, and each pin requires 3.1 ounces of gold and 7 hours of labour. Jewellery Junction has available 125 ounces of gold and 320 hours of labour. A bracelet sells for $1,650, a necklace for $850, and a pin for $790. How many of each item should be produced to maximize revenue? Ignore the fact that number of items must be integer. A. The antisans should make 13.60 units of bracelets, 12.67 units of necklaces and no pins B. The antisans should make no bracelets, 13.60 units of necklaces and 12.67 units of pins C. The antisans should make 13.60 units of bracelets, no necklaces and 12.67 units of pins D. The antisans should make 12.67 units of bracelets, no necklaces and 13.60 units of pins

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opportunity cost of making a necklace

Marisol is making bracelets and rings to sell at a craft fair. She plans to sell each bracelet for $6 and each ring for $8. The craft fair committee charges a $25 fee to sell at the fair, and it costs Marisol $2 to make a bracelet and $4 to make a ring. If Marisol wants to sell at least $600 in jewelry and spend less than $300 for supplies and the fee, which system of inequalities represents the situation? Let b represent the number of bracelets and r represent the number of rings.

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